We report on the experimental observation of interatomic Coulombic decay (ICD) in pure $^4$He nanoclusters of mean sizes between $N approx$ 5000 and 30000 and the subsequent scattering of energetic He$^+$ fragments inside the neutral cluster by using cold target recoil ion momentum spectroscopy. ICD is induced in He clusters by using vacuum ultraviolet light of $h u =$ 67 eV from the BESSY II synchrotron. The electronic decay creates two neighboring ions in the cluster at a well-defined distance. The measured fragment energies and angular correlations show that a main energy loss mechanism of these ions inside the cluster is a single hard binary collision with one atom of the cluster.